Also I would like to know whether the edges form a ring, is any algorithm available for it?

Would like to help, but the info you're providing is too vague to answer such detailed questions. How are your polygons defined? Could you post a small example of the data? If you post a list of ~10 polygon definitions and corresponding vertex definitions, I think you'll get some responses.

The polygon is defined as an .obj file. I have extracted the vertices and triangles.

That's a start. We are all familiar with .obj format. Could you post a small example of one of your .obj files and repeat your question(s) relative to the geometry in that file? You could probably get by with an .obj file containing 20 polys and their associated vertices.

Or - here's another approach. Can you compute and display the flat normals for the polys in one of your files? If you can do that, you can probably solve your problem.

Yes, I have vertices and triangle in obj file. I already calculated flat normals and vertex normals of each triangle.

Now check the angle between the flat normals of the triangles sharing an edge. If that angle is greater than some threshold angle (which you set), you have a sharp edge. This should be easy assuming that shared edges use the same vertices. For example, say Poly A is defined by vertices V1, V2, and V3, and Poly B is defined by vertices V1, V2, and V8. Polys A and B share edge V1-V2. Check the angle between the flat normals of Polys A and B. If it's greater than your threshold angle, you've identified a sharp edge. If edge V1-V2 is only used by one poly, it's an open edge and should be flagged differently.

Don't know what you mean by a 'ring'. Do you know what you mean by 'ring'?
If you can clearly define to yourself what you mean by a 'ring', you'll probably
be able to come up with an algorithm to find 'rings'.

Would help us to see an example of your geometry with one of the so-called 'rings' highlighted.

Sorry., I could not explain properly. Ring is formed when vertex v1 has edge with v2, v2 with v3......vn-1 with vn and vn with v1 again.

Again, that's only a start. There has to be a LOT more to it than that - otherwise you could find infinite rings in an object. In fact, every polygon is a ring by your definition. This is what I meant when I said you have to think carefully about what you mean by a 'ring'. If you can define it, you'll be able to compute it.

edit: so, i after asking my colleagues, i can say you need something they call a "for-loop" and some "if-statement"s.
i got lost in the discussion when someone said something about "compiling" and "linking".